Mathematics for Machine Learning (Wintersemester 2020/2021)

Lecturer: Prof. Dr. Christoph Lippert (Digital Health - Machine Learning) , Matthias Kirchler (Digital Health - Machine Learning)

General Information

• Weekly Hours: 4
• Credits: 6
• Graded: yes
• Enrolment Deadline: 01.10.2020 -20.11.2020
• Teaching Form: Lecture
• Enrolment Type: Compulsory Elective Module
• Course Language: English

Programs, Module Groups & Modules

Description

Both lectures and tutorials start in the second week only (i.e. from November 9th)!

Note that due to the online teaching format, there will be (asynchronous) online videos, but in exchange no lectures on Tuesdays (see format below)!

Course Moodle: https://hpi.de/friedrich/moodle/course/view.php?id=130
The course is also open to non-HPI students. If you don't have an HPI account to log into Moodle, send us a mail!

 

 

Machine learning uses tools from a variety of mathematical fields.

During this applied mathematics course, we cover a summary of the mathematical tools from linear algebra, calculus, optimization and probability theory that are commonly used in the context of machine learning. Beyond providing the solid mathematical foundation that is required for machine learning, we derive and discuss important machine learning concepts and algorithms.

Topic

Introduction

Vector Spaces, Linear maps

Metric spaces, Normed Spaces, Inner Product Spaces

Eigenvalues, Eigenvectors, Trace, Determinant

Orthogonal matrices, Symmetric matrices

Positive (semi-)definite matrices

Singular value decompositions, Fundamental Theorem of Linear Algebra

Operator and matrix norms

Low-rank approximation

Pseudoinverses, Matrix identities

Extrema, Gradients, Jacobian, Hessian, Matrix calculus

Taylor's theorem, Conditions for local minima

Gradient descent

Second order methods

Stochastic gradient descent

Convexity

Random Variables, Joint distributions

Great Expectations

Variance, Covariance, Random Vectors

Estimation of Parameters, Gaussian distribution

Frequentist vs. Bayesian Statistics

Expectation Maximization

Teaser in calculus of variations

Requirements

Basic knowledge in Analysis/Calculus und Linear Algebra (equivalent to Bachelor lecture Mathematics II)

Literature

https://gwthomas.github.io/docs/math4ml.pdf

https://mml-book.github.io/

Learning

Asynchronous lecture videos and exercise sessions via Zoom videoconferencing.

Materials and exercises will be managed over Moodle: https://hpi.de/friedrich/moodle/course/view.php?id=130
The course is also open to non-HPI students. If you don't have an HPI account to log into Moodle, send us a mail!

Examination

Written Exam at the end of the semester (100% of the grade).

Regular homework exercise sheets are required to be eligible for taking the exam (at least 50% of all points).

Dates

Lectures & Tutorials will start in the second week only (i.e. November 9th and November 11th)!

 

Lectures:

Contrary to the timetable, there will be no lecture on Tuesdays, but instead videos with the material (link on moodle).
Lectures on Wednesdays 9:15-10:45 will be held over Zoom (link on moodle) and be in a Q&A style, discussing the topics of the week.

 

Tutorials:

Mondays, 9:00 - 10:30 over Zoom (link on moodle)

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